Developing microphone array technologies for a small number of microphones is important due to the constraints of many devices. One direction to address this situation consists of virtually augmenting the number of microphone signals, e.g., based on several physical model assumptions. However, such assumptions are not necessarily met in realistic conditions. In this paper, as an alternative approach, we propose a neural network-based virtual microphone estimator (NN-VME). The NN-VME estimates virtual microphone signals directly in the time domain, by utilizing the precise estimation capability of the recent time-domain neural networks. We adopt a fully supervised learning framework that uses actual observations at the locations of the virtual microphones at training time. Consequently, the NN-VME can be trained using only multi-channel observations and thus directly on real recordings, avoiding the need for unrealistic physical model-based assumptions. Experiments on the CHiME-4 corpus show that the proposed NN-VME achieves high virtual microphone estimation performance even for real recordings and that a beamformer augmented with the NN-VME improves both the speech enhancement and recognition performance.